Programming Languages – Homework Assignment 2


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Programming Languages –
Homework Assignment 2

In this assignment, you will earn total 100 points. Here are some general instructions.
1. Read the problem descriptions and requirements carefully! There may be significant
penalties for not fulfilling the requirements.
2. Some problems ask you to explain the working of your function with the given input.
Your explanation must be consistent with your definition of the function. Your work
will be graded not only on the correctness of your answer, but also on the consistency
and clarity with which you express it.
3. This homework set is an individual homework, not a team-based effort. Discussion of
the concept is encouraged, but actual write-up of the solutions must be done individually and your final product – the code as well as the comments and explanations –
should never be shared.
4. Submit electronically exactly one file named YourLastName-YourFirstName-hw2.hs,
and nothing else, on
5. Make sure that the Haskell script (the .hs file) you submit compiles without any error
when compiled using the Glasgow Haskell Compilation System (ghc or ghci) version
7 and above1
If your program does not compile, you will receive very few points (more likely zero)
for this assignment. To avoid receiving zero for the entire assignment, if you cannot
complete defining a function correctly without compile error, you can set the function
definition undefined, see the skeleton code provided.
6. Remember to put the head comment in your file, including your name, UIN, and
acknowledgements of any help received in doing this assignment.
1Version 7 is installed in the departmental servers ( and, and
version 8 is what you will get if you install the Haskell system in your computer.
Below, the exercise problems are from the Haskell Textbook: “Programming in Haskell, 2nd
Ed.”, by Graham Hutton. Some problems are modified (with additional requirements) by
the instructor. Please read corresponding textbook chapters and the problem statements
carefully, paying attention to the requirements. For example, “using foldr, define . . . ”
means that using the foldr function when you define the assigned function is required.
There may be significant penalties for not fulfilling such requirements. Keep the name and
type of each function exactly the same as given in the problem statement and the skeleton
Problem 1. (5 points) Put your full name, UIN, and acknowledgements of any help received
in the head comment in your .hs file for this assignment.
Problem 2. (5 points) Chapter 4, Exercise 5. Using two nested conditional expressions in
the definition is a requirement.
Problem 3. (20 points) Chapter 4, Exercise 8.
Problem 4. (10 points) Chapter 5, Exercise 6. Using a list comprehension and factors
in the definition is a requirement. Include the definition of factors in your hw2.hs file (the
definition is in the text as well as in my lecture slides).
Problem 5. (7 + 7 + 6 = 20 points) Chapter 6, Exercise 5. Your answer should follow
the style of examples such as reverse, (++), insert, and zip in pages 62–64 in the text.
Write your answer neatly and clearly within a block comment {- · · · -}.
Problem 6. (15 points) This problem has two subproblems. In Assignment 1, Problems 5
and 6, you implemented merge sort that sorts a list in an ascending order.
1. (8 points) Define a recursive function mergeBy that merges two sorted lists by the
given criterion, for example, in an ascending order or in a descending order (so that
the resulting list is also sorted). The type signature of mergeBy is as follows.
mergeBy :: (a – a – Bool) – [a] – [a] – [a]
Notice the difference from merge :: Ord a = [a] – [a] – [a] in Ch. 6 Exercise 7 such that mergeBy accepts three arguments, the first of which is a comparison
function of type (a – a – Bool) that determines in which way the list is to be
sorted. Such comparison function that returns a Boolean value (true or false) is called
a predicate.
2. (7 points) Using mergeBy that you wrote above and halve that you wrote for Problem 6 in Assignment 1, define a recursive function msortBy. The problem specification
stays the same as that for msort in Ch. 6 Exercise 8, except the additional requirement
of the first argument being a predicate. Thus, the type of msortBy is:
msortBy :: (a – a – Bool) – [a] – [a]
Problem 7. (15 points) Chapter 7. Exercise 9.
1. (10 points) Define altMap.
altMap :: (a – b) – (a – b) – [a] – [b]
2. (5 points) Explain how your altMap works when it is applied as below.
altMap (*2) (‘div‘ 2) [0..6]
Problem 8. (10 points) Using map, filter, and (.) (function composition operator),
define a function that examines a list of strings, keeping only those whose length is odd,
converts them to upper case letters, and concatenates the results to produce a single string.
concatenateAndUpcaseOddLengthStrings :: [String] – String
You need to import Data.Char in order to use the toUpper function (see the skeleton
Have fun!

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